Parallelogram and Theorems

• Quadrilateral


  is a four-sided polygon with four edges and four corners
• Parallelogram


  is a quadrilateral with both pairs of opposite side parallel
• Theorem #1

  it is a parallelogram if the opposite sides are congruent
• Theorem #2


  it is a parallelogram if the opposite angles are congruent
• Theorem #3

  it is a parallelogram if the pairs of consecutive angles are supplementary
• Theorem #4

  it is a parallelogram if the diagonals bisect each other
• Quadrilaterals


  Parallelograms and Non-parallelograms
• Parallelogram


  A parallelogram is a quadrilateral with both pairs of opposite sides are parallel.
• Rectangle

  A rectangle is a parallelogram in which all of it angles are right angles.
• Theorem 5


  Diagonals of a rectangle are congruent.
• Rhombus


  It is a parallelogram in which all of its sides are congruent.
• Theorem 6

  Diagonals of a rhombus are perpendicular.
• Theorem 7

  In a rhombus, each diagonal bisects two of its angle.
• Square


  A square is a rectangle in which all its sides are congruent.
• Non-parallelogram


  A non-parallelogram is a quadrilateral with no equal opposite sides.
• Trapezoid


  It has only one pair of opposite sides parallel.
• Theorem 8

  If a trapezoid is isosceles, then the base angles are congruent.
• Theorem 9

  If the base angles of the trapezoid are congruent, then the trapezoid is isosceles.
• Theorem 10


  If a trapezoid is isosceles, then the diagonals are congruent
• Theorem 11


  If the diagonals of a trapezoid are congruent, then the trapezoid is isosceles.
• Theorem 12

  The mid segment of a triangle is parallel to the base of the triangle and its length is half as long as the base.
• Kite


  A kite is a quadrilateral with two pairs of congruent sides but no opposite sides are congruent.
• Quadrilaterals

  • Parallelograms
  • Rectangles, Rhombuses - Square
  • Non-parallelograms
  • Trapezoid
  • Kites
  • other quadrilaterals